Based on the calculations, for any number n > 1, [tex]|(\frac{1}{2} + \frac{3i}{4} )^n|[/tex] is less than one but not greater than or equal to one.
How to solve the equation?First of all, we would simplify the equation by using the lowest common multiple (LCM) of the fractions as follows:
[tex]|(\frac{2\;+\;3i}{4} )^n|[/tex]
By applying exponent rule, we have:
[tex](a.b)^n=a^n \times b^n\\\\|(\frac{(2\;+\;3i)^n}{4^n} )|\\\\|(\frac{(2\;+\;3i)^n}{(2^2)^n} )|[/tex]
By applying exponent power rule, we have:
[tex]|(\frac{(2\;+\;3i)^n}{2^{2n}} )|[/tex]
Assuming n = 2, we have:
[tex]|(\frac{(2\;+\;3i)^2}{2^{2\times 2}} )|\\\\|(\frac{(2\;+\;3i)^2}{2^{4}} )|\\\\|(\frac{-5\;+\;12i}{16} )|[/tex]
Therefore, for any number n > 1, [tex]|(\frac{1}{2} + \frac{3i}{4} )^n|[/tex] is less than one but not greater than or equal to one.
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PLSS HELP ME WITH THIS 15 POINTSS!
Answer:
D. y= 1/9x
Step-by-step explanation:
y= 1/9x
(x)=9y
so I think d is your answer sorry if its wrong but i hope i helped.
Answer: D. y= 1/9x
Step-by-step explanation: i think you answer is correct if not it's ok
what is a polygonomial
Answer:
See below
Step-by-step explanation:
Polynomials are sums of terms in the form of k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x²+2x-5 is a polynomial.
help please please 100pts no trolls please
Answer:
21.8 m/s
Step-by-step explanation:
Given that Tom drops a object from a height of h meters and it hits the ground with a veloc8of v m/s and it is given by function ;
[tex]\longrightarrow v =\sqrt{19.6h}[/tex]
We need to find out the velocity upon reaching the ground when it is dropped from a height of 24.3 m . On plugging in 24.3 in place of h we have ,
[tex]\longrightarrow v =\sqrt{19.6\times 24.3 }\ m/s\\\\\longrightarrow v =\sqrt{ 476.28} m/s \\\\\longrightarrow v = 21.823 \ m/s \\\\\longrightarrow \underline{\underline{ v = 21.8 \ m/s }}[/tex]
And we are done !
Answer:
21.8
Step-by-step explanation:
The formula is given :
v = √(19.6h)Given that h = 24.3 m, we need to find v.
Substituting the value of h in the formula :
v = √(19.6)(24.3)v = √476.28v = 21.8 m/s (nearest tenth)2. Answer each of the following based on the scenario below.
Scenario: You bought a brand new iphone 13 for $1,200. Unfortunately your phone
loses 10% of its value every year.
a. Does this scenario represent exponential growth or decay? De
b. What is the initial value of your phone? 2000
c. What is the growth/decay factor? 10
d. Create a function in exponential form that models how much your phone will be worth
after x years.
f(x) =
e. After 3 years how much will your phone be worth?
. After 8 years how much will your phone be worth?
a) losing value is exponential decay.
b) Initial value is the price you paid = $1,200
c) decay factor is 100% - the percent lost per year = 90%
d) value = starting value x decay factor^ time
f(x) = 1200 x 0.90^x
e) replace x with 3 then 8 and solve:
f(3) = 1200 x 0.90^3 = 874.80
after 3 years it is worth $874.80
f(8) = 1200 x 0.90^8 = 516.56
after 8 years it is worth $516.56
what is |3|?
please help i dont understand.
Answer:
Step-by-step explanation:
the bars, | |, mean absolute value
for example, if it was
| -9 |
then it would be 9
if it was
| 9 |
then it would be 9
if it was
| -550 |
it would be 550
you take the number, and if its negative, then it becomes positive
thats it
suppose you throw a ball straight up from the ground with a velocity of 224 feet per second. as the ball moves up, gravity slows it. eventually, the ball begins to fall back to the ground. the height h of thr ball after t seconds in the air is given by the equation h=-16t^2 + 224t. use the given information to answer.
a. find the height of the ball after four seconds. (type a whole number)
b. how long will it take the ball to reach a height of 768 ft?
c. how long after you throw the ball will it return to the ground? (type w whole number)
a. The height of the ball after four seconds is 640 ft
b. The time the ball reachs a height of 768 ft is 6 s or 8 s.
c. The time the ball reachs the ground after it is thrown is 14 seconds.
Since the height of the ball is a parabola, we need to know the equation parabola is
What is a parabola?A parabola is an equation of the form x(t) = at² + bt + c
a. Height of the ball after four secondsThe height of the ball after four seconds is 640 ft
Since the height of the ball is represented by the equation h(t) = -16t² + 224t. The height of the ball after four seconds is when t = 4.
So, h(t) = -16t² + 224t.
h(4) = -16(4)² + 224(4)
h(4) = -16(16) + 224(4)
h(4) = -256 + 896
h(4) = 640 ft
The height of the ball after four seconds is 640 ft
b. How long will it take the ball to reach a height of 768 ft?The time it takes the ball to reach a height of 768 ft is 6 s or 8 s.
To find this time, we substituie h = 768 into the equation for the height of the ball.
So, h(t) = -16t² + 224t
768 = -16t² + 224t.
16t² - 224t + 768 = 0
t² - 14t + 48 = 0
Using the quadratic formula, we find t
[tex]t = \frac{-(-14) +/- \sqrt{(-14)^{2} - 4 X 1 X 48} }{2 X 1} \\t = \frac{14 +/- \sqrt{196 - 192} }{2}\\t = \frac{14 +/- \sqrt{4} }{2}\\t = \frac{14 +/- 2 }{2}\\t = \frac{14 + 2 }{2} or t = \frac{14 - 2 }{2}\\t = \frac{16}{2} or t = \frac{12}{2}\\t = 8 or 6[/tex]
So, the time it takes the ball to reach a height of 768 ft is 6 s or 8 s.
c. How long after you throw the ball will it return to the ground?The time it takes the ball to reach the ground after it is thrown is 14 seconds.
To find the time it takes the ball to reach the ground, the height, h = 0.
So, h(t) = 0
-16t² + 224t = 0
-16t(t - 14) = 0
t(t - 14) = 0
t = 0 or t - 14 = 0
t = 0 or t = 14 s
So, the time it takes the ball to reach the ground after it is thrown is 14 seconds.
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Solve for x 5.2³x = 21.
Answer:
D) 0.69
Step-by-step explanation:
Given :
5 × 2³ˣ = 21
Divide by 5 on each side :
1/5 x 5 x 2³ˣ = 1/5 x 212³ˣ = 4.2Taking the cubic root :
∛2³ˣ = ∛4.22ˣ = 1.61Using logarithm values :
log(2ˣ) = log(1.61)x log(2) = log(1.61)x = log (1.61) / log (2)x = log₂ (1.61)x = 0.69 (approximately)Answer:
D. 0.69
Step-by-step explanation:
Given equation:
[tex]5 \cdot 2^{3x}=21[/tex]
Divide both sides by 5:
[tex]\implies \dfrac{5 \cdot 2^{3x}}{5}=\dfrac{21}{5}[/tex]
[tex]\implies2^{3x}=4.2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies(2^3)^x=4.2[/tex]
[tex]\implies8^x=4.2[/tex]
Take natural logs of both sides:
[tex]\implies \ln 8^x=\ln 4.2[/tex]
[tex]\textsf{Apply the log Power law} \quad \ln x^n=n\ln x :[/tex]
[tex]\implies x \ln 8=\ln 4.2[/tex]
Divide both sides by ln 8:
[tex]\implies \dfrac{x \ln 8}{\ln 8}=\dfrac{\ln 4.2}{\ln 8}[/tex]
[tex]\implies x=\dfrac{\ln 4.2}{\ln 8}[/tex]
[tex]\implies x=0.690129776...[/tex]
[tex]\implies x=0.69 \: \sf (2\:dp)[/tex]
A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.
an = 2(an − 1 + 4) and a1 = 5 (the n and n-1 is suppose to be a subscript, I just can't figure out how to make it like that)
So
a_2
2a_1+8=2(5)+8=18a_3
2a_2+8=2(18)+8=44a_4
2a_3+8=2(44)+8=96a_5
2a_4+8=2(96)+8=200If x = 7 units, y = 5 units, and h = 3 units, then what is the area of the parallelogram shown above?
Answer:
Step-by-step explanation:
21u²The formula for the area of a parallelogram is base times height
so
x = 7 (base)
y = 5
h = 3 (height)
7 * 3 =
21u²
Ms. Jones baked 12 cookies on Monday. On Tuesday, she baked 15 cookies, on Wednesday, she baked 18 cookies. If Ms. Jones continues baking cookies this way, how many will she bake on Friday?
Answer:
19 or 20
Step-by-step explanation:
well is see
Monday = 12
Tuesday = 12 + 3 = 15
Wednesday = 15 +3 = 18
so the pattern is 3
but now since there is only 14, 13, 19, and 20
we could say she only added 1 or 1 each time
because it said she wanted cookies to stay about 18
1 x 2 = 2
18 + 2 = 20
or
1 + 18
19
sorry if it's wrong
wich one is greatest?
A. 2.3 x 10
B. 8.6 x 10
C. 1.2 x 10
D. 3,600
Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1?
Using the normal distribution, it is found that 16.43% of adults in the US qualify for stage 1.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Researching the problem on the internet, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 122, \sigma = 22[/tex].
The proportion of adults in the US qualify for stage 1 is the p-value of Z when X = 160 subtracted by the p-value of Z when X = 140, hence:
X = 160:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{160 - 122}{22}[/tex]
Z = 1.73
Z = 1.73 has a p-value of 0.9582.
X = 140:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 122}{22}[/tex]
Z = 0.82
Z = 0.82 has a p-value of 0.7939.
0.9582 - 0.7939 = 0.1643.
0.1643 = 16.43% of adults in the US qualify for stage 1.
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A theater has 18 rows of seats. Each row has the same number of seats.
Suppose there were 3 fewer rows. Then for the theater to hold the same
number of people, each remaining row would need 6 more seats. How
many seats are in the theater?
There are a total of 180 seats in the theater
How to determine the number of seats?The theatre illustrates an arithmetic sequence, with the following parameters:
Number of rows = 18
Let the number of seats per row be n.
So, we have:
Total = 18n
When there are 3 fewer rows, the total number of seats is:
Total = (18 - 3) * (n + 6)
This gives
Total = 15* (n + 6)
Substitute Total = 18n in Total = 15* (n + 6)
18n = 15* (n + 6)
Open the bracket
18n = 15n + 90
Subtract 15n from both sides
3n = 30
Divide both sides by 3
n = 10
Substitute n = 10 in Total = 18n
Total = 18 *10
This gives
Total = 180
Hence, there are 180 seats in the theater
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Select the correct answer. What is the solution to |x − 4| ≥ 7? A. -3 ≤ x ≤ 11 B. -11 ≤ x ≤ 3 C. x ≥ 11 or x ≤ -3 D. x ≥ 3 or x ≤ -11
Answer:
C) x ≥ 11 or x ≤ -3
Explanation:
Given following: |x − 4| ≥ 7
Apply absolute rule: If |u| ≥ 0 then u ≤ -a, u ≥ a
Solving stepwise:
⇒ x - 4 ≤ -7, x - 4 ≥ 7
change sides
⇒ x ≤ -7 + 4, x ≥ 7 + 4
add/subtract integers
⇒ x ≤ -3, x ≥ 11
Answer:
x ≥ 11 or x ≤ -3
Step-by-step explanation:
Hi there! Please take a look at the following explanation and let me know in comment if you have any questions!
Given:[tex]\displaystyle \large{|x-4|\geq 7}[/tex]
To solve an absolute inequality, consider the following theorems.
Theorems:For b ≥ 0:
(1) If |x-a| ≥ b then we have x-a ≥ b or x-a ≤ -b so that we end up with x ≥ b+a, x ≤ -b+a
(2) If |x-a| ≤ b then we have -b ≤ x-a ≤ b which can be simplified to -b+a ≤ x ≤ b+a
Step:From the inequality, we use the (1) theorem.
[tex]\displaystyle \large{x-4\geq 7, x-4\leq -7}\\\\\displaystyle \large{x\geq 7+4, x\leq -7+4}\\\\\displaystyle \large{x\geq 11, x \leq -3}[/tex]
Therefore, the answer is x ≥ 11 or x ≤ -3
Drag and drop to complete the proof below:
Given: DE is tangent to circle C, at point F
Prove:
E
D
F
חד
C
The proof of the given statements is shown below:
What is tangent to a circle?A line segment which touches a circle specified to only one point is called a tangent to that circle.
1. given
2. A line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.
3. Since the tangent is perpendicular to radius i.e., EFC is right angle then,
angle EFC =90
4. Sum of interior angles of a triangle is 180°.
5. proved above: angle EFC= 90
6. FEC + ECF= 180-90=90
7. As proved above
FEC + ECF=90, its shows that angle FEC and ECF are complementary angle.
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Enter the range of values for x:
2x-4
10
45
60
2
Answer:
the answer is 0
Step-by-step explanation:
2x-4
putting 10
2x10-4
20-4
=16
putting 45
2x45-4
90-4
=86
putting 60
60x2-4
120-4
=116
putting 2
2x2=4
4-4=0
PLEASE HELP AREA QUESTION 40 POINTS
Answer:
14 meters
Step-by-step explanation:
Please help me, I’m only five more questions away from being done
Answer:
[tex] {2t}^{3} + {20t}^{2} - 2t + 15[/tex]
Hope this helps!!
colleen is searching online for airline tickets. Two weeks ago, the cost to fly from boston to hartford was $200. now its cost $340. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answer:
A) 70%
B) 95%
Step-by-step explanation:
A) $200 to $340
Increase = $340 - $200 = $140
Percentage of increase = $140/$200 * 100% = 70%
B) Additional $50
Increase = $140 + $50 = $190
Percentage of increase = $190/$200 * 100% = 95%
Have to make the equation on the left look like the equation on the right. There are apparently only 2 steps but I can not figure it out for myself. Also not supposed to touch the second equation just show how you get it from the first.
Step-by-step explanation:
[tex] \frac{a}{b} c = \frac{a}{ \frac{b}{c} } [/tex]
[tex] \frac{a}{b} c = a \times \frac{c}{b} [/tex]
Answer:
Step-by-step explanation: change A/B/C to A÷B/C then change the division sign into a multiplicmultiplication sign so that you will have A×C/Bwhich will make your left equation = to your right equation
In parallelogram JKLM if m/JKL-150° find m/LMJ.
Answer:
150 degrees
Step-by-step explanation:
This is because the opposite angles in this parallelogram are equal.
Solve for x. Round to the nearest tenth.
Answer:
x= 11.87
Step-by-step explanation:
sec(32) = 14 /x
1.18=14/x
x1.18 =14
x= 11.87
here is the histogram of a data distribution. all class widths are 1. which of the following numbers is closest to the mean of this distribution a)3 b)5 c)4 d)9 e)7
The number 5 is closest to the mean of the distribution, option (B) is correct.
What is mean?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
From the histogram:
2, 6, 4, 2, 0, 1, 6, 4, 2, 1
The sum of the above data = 28
= 2×1+6×2+4×3+2×4+0×5+1×6+6×7+4×8+2×9+1×10
= 2+12+12+8+6+42+32+18+10
= 142
Mean = 142/28
= 5.07
Thus, the number 5 is closest to the mean of the distribution option (B) is correct.
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Answer:4
Step-by-step explanation:jus done this question
If you solve this i give you 50 points
Step-by-step explanation:
2) 8,6,5,3 ,57 7,4,2/8
=92/8
mean =11.5
Arrange the terms in ascending order
2,3, 4, 5, 6, 7, 8, 57
the median of the ascending set= 5.5
3) 72 75 85 82 37 108/ 6
459/6
mean =76.5
Arrange the terms in ascending order
37, 72, 75, 82, 85, 108
the median of the ascending set= 78.5
4) 10 students were asked because there were 10 data values in the list.
5) it should be 55/10 =5.5
so its false
6) Sum first and find the mean number
5+4+3+2+1/5
=3
What is 2/8 in its simplest form
Answer:
14
Step-by-step explanation: because you find a common number that both the numerator and the denominator can be divided by. In this case, it is 2 . You can't divide 14 anymore so that is the final answer.
What is the surface area of the box formed by the pattern below?
Answer:
S.A = 2( L×W+W×H+ H×L)
= 2(2×4+4×1+1×2)
= 2(8+4+2)
2(14)
= 2×14= 28
Step-by-step explanation:
answer 28
Anyone? please help asap i really want to finish this
It is a Part A and Part B Question
Note: please add the answer next to what part it's from so I can know which part was answered
Step-by-step explanation:
oh, come on ! one is finding the inequality itself, the other is solving it. you don't know the difference of that ?
if so, please let me know, what you don't understand of the following explanations, so that I can add whatever is necessary.
you know, what an equality (ahem, equation) is ?
both, equations and inequalities are like a balancing scale with usual different things on the two pans left and right.
an equation is when both sides are in balance. their weight is equal.
an inequality is, when one side is heavier than the other.
and you know, what a variable is ? it is a kind of placeholder for actual values. it is like keeping some space open on the scale pan with a list of conditions for what kind of things you can put in that open space, so that the status of the scale stays unchanged.
A
twenty less than a number is at least 15
looks mathematically
x - 20 >= 15 (larger or equal = "at least")
B
x - 20 >= 15
x >= 35
so, this is true for
{x € R | x >= 35}
or
{x € R | x = 35 or x > 35}
so, this is true for all real values of x that are at least 35.
anyone understand this?
Hi guys !
Find the missing angle in the given figure .
All the best *
Answer:
third angle: 50°
Explanation:The interior angles of a triangle sum ups to 180°.
Here given two angles: 95°, 35°, x - Let the missing angle be x
When they sum up, they equal to 180:
x + 35 + 95 = 180
x + 130 = 180
x = 180 - 130
x = 50
Given two angles are 35° and 95°
Let the unknown angle be "x"
We know that sum of angles of a triangle is 180°
Therefore,
[tex]\sf{35°+95° + x = 180°}[/tex]
[tex]\sf{130° + x = 180°}[/tex]
[tex]\sf{x = 180°-130°}[/tex]
[tex]\sf{x = 50°}[/tex]
Hence, the missing angle is 50°.
What is the volume of this rectangular prism?
Answer:
180cm
Step-by-step explanation:
To find the volume you do Length times Width times Height
use this it'll help when you run into this again, it's formula is just
LxWxH, in this order good luck!